Problem: Simplify the following expression and state the condition under which the simplification is valid. $t = \dfrac{y^2 - 4}{y - 2}$
Solution: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = y$ $ b = \sqrt{4} = -2$ So we can rewrite the expression as: $t = \dfrac{({y} {-2})({y} + {2})} {y - 2} $ We can divide the numerator and denominator by $(y - 2)$ on condition that $y \neq 2$ Therefore $t = y + 2; y \neq 2$